

A346133


Numbers N = A * B such that N (reversed digits) = A (reversed digits) * B (reversed digits). A singledigit number is its own reversal and neither A nor B has a leading zero. No pair (A, B) has both A and B palindromic or simpledigit. The reversed products are not included in the sequence.


3



24, 26, 28, 36, 39, 46, 48, 68, 69, 132, 143, 144, 154, 156, 165, 168, 169, 176, 187, 198, 204, 206, 208, 224, 226, 228, 244, 246, 248, 252, 253, 264, 266, 268, 273, 275, 276, 284, 286, 288, 294, 297, 299, 306, 309, 336, 339, 366, 369, 374, 384, 385, 396, 399
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..54.


EXAMPLE

a(1) = 24 = 2 * 12 and 2 * 21 = 42 (which is 24 reversed);
a(2) = 26 = 2 * 13 and 2 * 31 = 62 (which is 26 reversed);
a(3) = 28 = 2 * 14 and 2 * 41 = 82 (which is 28 reversed);
a(4) = 36 = 3 * 12 and 3 * 21 = 63 (which is 36 reversed); etc.


MATHEMATICA

q[n_] := IntegerReverse[n] >= n && AnyTrue[Rest @ Take[(d = Divisors[n]), Ceiling[Length[d]/2]], (# > 9  n/# > 9) && !Divisible[#, 10] && !Divisible[n/#, 10] && (!PalindromeQ[#]  !PalindromeQ[n/#]) && IntegerReverse[#] * IntegerReverse[n/#] == IntegerReverse[n] &]; Select[Range[2, 400], q] (* Amiram Eldar, Jul 07 2021 *)


PROG

(Python)
from sympy import divisors
def rev(n): return int(str(n)[::1])
def ok(n):
divs = divisors(n)
for a in divs[1:(len(divs)+1)//2]:
b = n // a
reva, revb, revn = rev(a), rev(b), rev(n)
if revn < n or a%10 == 0 or b%10 == 0: continue
if (reva != a or revb != b) and revn == reva * revb: return True
return False
print(list(filter(ok, range(400)))) # Michael S. Branicky, Jul 06 2021


CROSSREFS

Cf. A066531.
Sequence in context: A241042 A346290 A097376 * A079720 A053680 A260251
Adjacent sequences: A346130 A346131 A346132 * A346134 A346135 A346136


KEYWORD

base,nonn


AUTHOR

Eric Angelini and Carole Dubois, Jul 05 2021


STATUS

approved



